Aww, Ryme changed the quest while I was keeping records on it.
Oh well. If anyone is interested, I discovered that the Demiurge appeared after I defeated 4 Archons, and that Archons cannot be lasso'd or voodoo'd. That led me to believe that the quest mechanic was similar to how you met Susan: defeat 4 protest instigators to unlock the NC in which you meet Susan.
But now all of that effort is rendered obsolete.
EDIT: Corrected a typo.
Curse you its and it's! Curse yoooooooooou!